## Cantilever Beam - Theory vs Elmer results

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asandip
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### Cantilever Beam - Theory vs Elmer results

Hello,

I am looking to determine the mass, stress and displacement of a cantilever beam subjected to horizontal and vertical loads at its free end. The theoretical model is attached with this message.

I have been using the files from tutorial 3 in the Elmer GUI Manual - Linear Elasticity/Cantilever Beam/beam3d.grd. The displacement values compare well (theory vs Elmer). How do I solve for the mass? The Linear elasticity solver solves for displacement and stress, but I couldn't find an option for mass.

Also, which of the Elmer stress (von mises/stress in xx/stress in yy, etc.) values should I compare with the theoretical stress value?

Thank you for any information you can provide.

- Anjali
Attachments
Cantilever Beam Theoretical Model.PNG

kevinarden
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### Re: Cantilever Beam - Theory vs Elmer results

Your equations are calculating normal X stress so you would compare to XX. Not sure if Elmer outputs mass, total mass is not required to solve the linear static problem unless a gravity load is used. If you run a case with just a 1G body force then the reaction force is equal to the mass.

asandip
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### Re: Cantilever Beam - Theory vs Elmer results

Thank you for your response. Had one follow up question - in the equation there is also the Y components, so would I need to compare it with XX + YY?

kevinarden
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### Re: Cantilever Beam - Theory vs Elmer results

After studying your equations further, the beams length must be in the Z direction, therefore the normal bending stress is ZZ. X is the width, and t is the Y direction. The horizontal load produces bending about the Y axis, and the vertical load produces bending about the X axis, both bending stresses add together at point 1 (see sketch), but the stresses are in the ZZ direction. Also your stress equation appears to assume that L = 100. Comments on weight versus mass also included in the attached. Elmer and most FEA codes use mass units not weight units.
beam.PNG

asandip
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### Re: Cantilever Beam - Theory vs Elmer results

Thank you so much for sharing the derivation!

asandip
Posts: 86
Joined: 09 May 2019, 22:06
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### Re: Cantilever Beam - Theory vs Elmer results

Hello,

I had a follow up question. I am looking to extract force in the y direction for this problem. I tried the following in the save scalars/variable -
force 2
Force 2
force 2 Real
Force 2 Real
Stress bodyforce 2
stress bodyforce 2

For all of the above, I get the same error - "Requested variable does not exist". How can I resolve this problem?

Thank you.

- Anjali

kevinarden
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### Re: Cantilever Beam - Theory vs Elmer results

I looked at the code and there is
ForceVector
LocalForce
LocalExternalForce

asandip
Posts: 86
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### Re: Cantilever Beam - Theory vs Elmer results

Hello,

Thank you for your response.

I tried the terms taht you had suggested but for some reason I am getting the same error - "Requested variable does not exist". I am not sure what I am missing.

Please find my .sif attached with this email. Thank your for your time and consideration.

- Anjali
Attachments
case.sif

kevinarden
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### Re: Cantilever Beam - Theory vs Elmer results

Sorry I can be of no more help, the calculated variable names and output variable names are not well published for Elmer. The input variable names are in the Elmer Models manual, sometimes they are the same and sometimes they are not.

raback
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### Re: Cantilever Beam - Theory vs Elmer results

Hi

If you want to use save scalars then mass would be "operator 1 = volume" times the density. I think you can give volume "coeffcient 1 = density" to get the mass.

As forces go, you could compute stresses and the take an "boundary int" over the desired stress component. Or you could calculate the reaction forces by "Calcalate loads = True" and sum over the resulting nodal forces to get force on a boundary,

-Peter